Question

Student X and Student Y are both studying for a test. Student X studies 2 hours every day, while Student Y starts studying 4 days after Student X and studies 3 hours each day. Define a variable and write an equation that represents the information given. Determine the number of days after Student X starts studying when both students will have studied the same number of hours.

Answer 1

Answer: Let's define the variable t as the number of days after Student X starts studying.

Then the equation that represents the total number of hours each student has studied in terms of t is:

For Student X: Hx = 2t

For Student Y: Hy = 3(t-4)

Note that we subtract 4 from t for Student Y since they start studying 4 days after Student X.

To find the number of days after Student X starts studying when both students will have studied the same number of hours, we can set the two equations equal to each other and solve for t:

2t = 3(t-4)

2t = 3t - 12

t = 12

Therefore, it will take 12 days after Student X starts studying for both students to have studied the same number of hours.

Explanation:

Answer 2

Let's define the variable "d" to represent the number of days after Student X starts studying when both students will have studied the same number of hours.

Student X will study for d days, and since they study 2 hours each day, they will have studied a total of:

2d hours

Student Y will start studying 4 days after Student X, so by the time Student Y starts studying, Student X will have already studied for d + 4 days.

Student Y will study for d days, and since they study 3 hours each day, they will have studied a total of:

3d hours

To find the number of days when both students will have studied the same number of hours, we can set the two expressions for total hours equal to each other and solve for d:

2d = 3d - 12

Adding 12 to both sides:

2d + 12 = 3d

Subtracting 2d from both sides:

12 = d

Therefore, both students will have studied the same number of hours 12 days after Student X starts studying.

Explanation: